(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ok so a piano tuner plays an out of tune A note on his piano and then strikes his 440 hz tuning fork. He notices a beat of 2 Hz. When he loosens the piano string and plays the note again, the beat goes to 4 hz. What was the frequency of the note before he loosened the string? a.438 b. 440 c. 442. d. 444

2. Relevant equations

f1-f2=beat f

v=square root of T/m/L

3. The attempt at a solutionOk so I know that its either 442 or 438Hz since the only way I can get 2 beats is 440-438 or 442-440. I also know that the string is loosen then T must go down and since its proportion to v, then v must go down also. Since v=fλ and since λ stays constant since the sting length does not change then frequency must go down. That means that the final frequency must be lower than 440 because if it was higher it would have to go up to 444. If its 440-436= 4hz and this means that the starting note had to be below 440. Is this the right way to think about? And I don't understand the relationship between change in v with change in beat frequency? For example in V goes up should beat f go up and vice versa.

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# Homework Help: Beats on Piano string

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